%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP421-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:33:50 PM UTC 2026
% Result : Unsatisfiable 4.13s 0.93s
% Output : CNFRefutation 4.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 6
% Syntax : Number of formulae : 37 ( 37 unt; 4 def)
% Number of atoms : 37 ( 36 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 11 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 37 ( 37 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C] : inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(B),multiply(inverse(C),inverse(multiply(inverse(C),C))))))),multiply(A,C))) = B,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,plain,
! [X0,X1,X2] : inverse(multiply(inverse(multiply(X0,inverse(multiply(inverse(X1),multiply(inverse(X2),inverse(multiply(inverse(X2),X2))))))),multiply(X0,X2))) = X1,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f4,plain,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f5,definition,
sF1_fnc = inverse(a1),
introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition]) ).
fof(f6,definition,
sF0_fnc = multiply(sF1_fnc,a1),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f7,definition,
sF3_fnc = inverse(b1),
introduced(definition,[new_symbols(definition,[sF3_fnc])],[function_definition]) ).
fof(f8,definition,
sF2_fnc = multiply(sF3_fnc,b1),
introduced(definition,[new_symbols(definition,[sF2_fnc])],[function_definition]) ).
fof(f9,plain,
sF0_fnc != sF2_fnc,
inference(definition_folding,[],[f4,f8,f7,f6,f5]) ).
fof(f10,plain,
! [X0,X1,X2] : inverse(multiply(inverse(multiply(X0,X1)),multiply(X0,X2))) = multiply(inverse(X2),inverse(multiply(inverse(X1),multiply(inverse(inverse(multiply(inverse(X2),X2))),inverse(multiply(inverse(inverse(multiply(inverse(X2),X2))),inverse(multiply(inverse(X2),X2)))))))),
inference(paramodulation,[status(thm)],[f3,f3]) ).
fof(f16,plain,
! [X0,X1] : inverse(multiply(inverse(multiply(X0,inverse(multiply(inverse(X1),multiply(sF1_fnc,inverse(multiply(inverse(a1),a1))))))),multiply(X0,a1))) = X1,
inference(paramodulation,[status(thm)],[f5,f3]) ).
fof(f21,plain,
! [X0] : inverse(multiply(inverse(multiply(sF1_fnc,inverse(multiply(inverse(X0),multiply(inverse(a1),inverse(multiply(inverse(a1),a1))))))),sF0_fnc)) = X0,
inference(paramodulation,[status(thm)],[f6,f3]) ).
fof(f25,plain,
! [X0,X1] : inverse(multiply(inverse(multiply(X0,inverse(multiply(inverse(X1),multiply(sF1_fnc,inverse(multiply(sF1_fnc,a1))))))),multiply(X0,a1))) = X1,
inference(forward_demodulation,[status(thm)],[f5,f16]) ).
fof(f26,plain,
! [X0,X1] : inverse(multiply(inverse(multiply(X0,inverse(multiply(inverse(X1),multiply(sF1_fnc,inverse(sF0_fnc)))))),multiply(X0,a1))) = X1,
inference(forward_demodulation,[status(thm)],[f6,f25]) ).
fof(f35,plain,
! [X0] : inverse(multiply(inverse(multiply(sF1_fnc,inverse(multiply(inverse(X0),multiply(sF1_fnc,inverse(multiply(inverse(a1),a1))))))),sF0_fnc)) = X0,
inference(forward_demodulation,[status(thm)],[f5,f21]) ).
fof(f36,plain,
! [X0] : inverse(multiply(inverse(multiply(sF1_fnc,inverse(multiply(inverse(X0),multiply(sF1_fnc,inverse(multiply(sF1_fnc,a1))))))),sF0_fnc)) = X0,
inference(forward_demodulation,[status(thm)],[f5,f35]) ).
fof(f37,plain,
! [X0] : inverse(multiply(inverse(multiply(sF1_fnc,inverse(multiply(inverse(X0),multiply(sF1_fnc,inverse(sF0_fnc)))))),sF0_fnc)) = X0,
inference(forward_demodulation,[status(thm)],[f6,f36]) ).
fof(f49,plain,
! [X0] : inverse(multiply(inverse(multiply(sF1_fnc,inverse(multiply(X0,multiply(sF1_fnc,inverse(sF0_fnc)))))),sF0_fnc)) = multiply(inverse(multiply(sF1_fnc,inverse(multiply(inverse(X0),multiply(sF1_fnc,inverse(sF0_fnc)))))),sF0_fnc),
inference(paramodulation,[status(thm)],[f37,f37]) ).
fof(f52,plain,
inverse(multiply(inverse(multiply(sF1_fnc,inverse(multiply(sF3_fnc,multiply(sF1_fnc,inverse(sF0_fnc)))))),sF0_fnc)) = b1,
inference(paramodulation,[status(thm)],[f7,f37]) ).
fof(f53,plain,
inverse(multiply(inverse(multiply(sF1_fnc,inverse(multiply(sF1_fnc,multiply(sF1_fnc,inverse(sF0_fnc)))))),sF0_fnc)) = a1,
inference(paramodulation,[status(thm)],[f5,f37]) ).
fof(f143,plain,
! [X0,X1,X2,X3] : inverse(multiply(inverse(multiply(X0,X1)),multiply(X0,X2))) = inverse(multiply(inverse(multiply(X3,X1)),multiply(X3,X2))),
inference(paramodulation,[status(thm)],[f10,f10]) ).
fof(f669,plain,
! [X0,X1,X2,X3,X4] : inverse(multiply(inverse(multiply(X0,inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),multiply(X1,X3))),multiply(sF1_fnc,inverse(sF0_fnc)))))),multiply(X0,a1))) = multiply(inverse(multiply(X4,X2)),multiply(X4,X3)),
inference(paramodulation,[status(thm)],[f143,f26]) ).
fof(f715,plain,
! [X0,X1,X2,X3] : multiply(inverse(multiply(X0,X1)),multiply(X0,X2)) = multiply(inverse(multiply(X3,X1)),multiply(X3,X2)),
inference(forward_demodulation,[status(thm)],[f26,f669]) ).
fof(f728,plain,
! [X0,X1] : multiply(a1,multiply(inverse(multiply(sF1_fnc,inverse(multiply(sF1_fnc,multiply(sF1_fnc,inverse(sF0_fnc)))))),X0)) = multiply(inverse(multiply(X1,sF0_fnc)),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f53,f715]) ).
fof(f4042,plain,
multiply(inverse(multiply(sF1_fnc,inverse(multiply(inverse(sF1_fnc),multiply(sF1_fnc,inverse(sF0_fnc)))))),sF0_fnc) = a1,
inference(backward_demodulation,[status(thm)],[f49,f53]) ).
fof(f4043,plain,
multiply(inverse(multiply(sF1_fnc,inverse(multiply(inverse(sF3_fnc),multiply(sF1_fnc,inverse(sF0_fnc)))))),sF0_fnc) = b1,
inference(backward_demodulation,[status(thm)],[f49,f52]) ).
fof(f4044,plain,
! [X0] : multiply(inverse(multiply(sF1_fnc,inverse(multiply(inverse(inverse(X0)),multiply(sF1_fnc,inverse(sF0_fnc)))))),sF0_fnc) = X0,
inference(backward_demodulation,[status(thm)],[f49,f37]) ).
fof(f6103,plain,
multiply(a1,multiply(inverse(multiply(sF1_fnc,inverse(multiply(sF1_fnc,multiply(sF1_fnc,inverse(sF0_fnc)))))),sF0_fnc)) = multiply(inverse(multiply(inverse(multiply(sF1_fnc,inverse(multiply(inverse(sF3_fnc),multiply(sF1_fnc,inverse(sF0_fnc)))))),sF0_fnc)),b1),
inference(paramodulation,[status(thm)],[f4043,f728]) ).
fof(f6192,plain,
multiply(a1,multiply(inverse(multiply(sF1_fnc,inverse(multiply(sF1_fnc,multiply(sF1_fnc,inverse(sF0_fnc)))))),sF0_fnc)) = multiply(multiply(inverse(multiply(sF1_fnc,inverse(multiply(inverse(inverse(sF3_fnc)),multiply(sF1_fnc,inverse(sF0_fnc)))))),sF0_fnc),b1),
inference(forward_demodulation,[status(thm)],[f49,f6103]) ).
fof(f6193,plain,
multiply(a1,multiply(inverse(multiply(sF1_fnc,inverse(multiply(sF1_fnc,multiply(sF1_fnc,inverse(sF0_fnc)))))),sF0_fnc)) = multiply(sF3_fnc,b1),
inference(forward_demodulation,[status(thm)],[f4044,f6192]) ).
fof(f6194,plain,
multiply(a1,multiply(inverse(multiply(sF1_fnc,inverse(multiply(sF1_fnc,multiply(sF1_fnc,inverse(sF0_fnc)))))),sF0_fnc)) = sF2_fnc,
inference(forward_demodulation,[status(thm)],[f8,f6193]) ).
fof(f6205,plain,
! [X0] : multiply(inverse(multiply(X0,sF0_fnc)),multiply(X0,sF0_fnc)) = sF2_fnc,
inference(paramodulation,[status(thm)],[f728,f6194]) ).
fof(f6256,plain,
multiply(inverse(a1),multiply(inverse(multiply(sF1_fnc,inverse(multiply(inverse(sF1_fnc),multiply(sF1_fnc,inverse(sF0_fnc)))))),sF0_fnc)) = sF2_fnc,
inference(paramodulation,[status(thm)],[f4042,f6205]) ).
fof(f6306,plain,
multiply(sF1_fnc,multiply(inverse(multiply(sF1_fnc,inverse(multiply(inverse(sF1_fnc),multiply(sF1_fnc,inverse(sF0_fnc)))))),sF0_fnc)) = sF2_fnc,
inference(forward_demodulation,[status(thm)],[f5,f6256]) ).
fof(f6307,plain,
multiply(sF1_fnc,a1) = sF2_fnc,
inference(forward_demodulation,[status(thm)],[f4042,f6306]) ).
fof(f6308,plain,
sF0_fnc = sF2_fnc,
inference(forward_demodulation,[status(thm)],[f6,f6307]) ).
fof(f6309,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f6308,f9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP421-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n020.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 20:14:02 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.13/0.37 % Drodi V4.1.1
% 4.13/0.93 % Refutation found
% 4.13/0.93 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 4.13/0.93 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 4.13/0.99 % Elapsed time: 0.610827 seconds
% 4.13/0.99 % CPU time: 4.577143 seconds
% 4.13/0.99 % Total memory used: 152.735 MB
% 4.13/0.99 % Net memory used: 150.800 MB
%------------------------------------------------------------------------------